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arxiv: 2605.12482 · v2 · pith:OMDMAB5Anew · submitted 2026-05-12 · 🌌 astro-ph.CO · gr-qc

Unveiling f(R) Gravity with Void-Galaxy Cross-Correlation Multipoles

Yue Nan This is my paper

Pith reviewed 2026-05-20 21:27 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc
keywords f(R) gravitycosmic voidsredshift-space distortionsvoid-galaxy cross-correlationHu-Sawicki modelmodified gravitymultipole moments
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0 comments X

The pith

Redshift-space void-galaxy multipoles reveal size-dependent f(R) gravity deviations

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper calculates the monopole, dipole, and quadrupole of the void-galaxy cross-correlation in redshift space for Hu-Sawicki f(R) gravity. It finds that the monopole deviation from standard cosmology increases sharply for smaller voids due to the scalaron's limited range of about 8 Mpc/h. Nonlinear evolution around void boundaries boosts the signal by a factor of roughly 4, potentially making it detectable with surveys like DESI and Euclid. Readers would care if this provides a practical way to test modified gravity in unscreened low-density regions.

Core claim

The monopole deviation from ΛCDM grows from +2.8% for large voids with r_v=30 h^{-1}Mpc to +29.7% for small voids with r_v=11.7 h^{-1}Mpc at |f_R0|=10^{-5}. This size-dependent signature arises from the Compton-scale scalaron response with λ_C ≈ 8 h^{-1}Mpc. Nonlinear evolution amplifies the modified-gravity signal by A_0 ≈ 4. The gravitational potential includes a finite-range Yukawa component that produces a radially dependent dipole signature.

What carries the argument

Semi-analytical framework combining scale-dependent growth induced by the scalaron with nonlinear spherical shell dynamics for the Hu-Sawicki f(R) model in the quasi-static limit

If this is right

  • The modified gravity signal becomes accessible to ongoing and upcoming spectroscopic surveys such as DESI, Subaru PFS, Euclid, and Roman.
  • The Yukawa component in the potential yields a radially dependent dipole that complements the density and velocity multipoles.
  • The overall signal tends to weaken at higher redshifts but could still be detected in Stage-IV void samples.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar calculations could apply to other modified gravity models if their effective G(k,a) is specified in the quasi-static regime.
  • Void size selection might allow mapping the characteristic scale of the fifth force.
  • Joint analysis of multipoles could help separate fifth-force effects from standard dark energy inhomogeneities.

Load-bearing premise

The approach relies on the quasi-static limit to define the effective gravitational coupling and on nonlinear spherical shell dynamics applied to the Hu-Sawicki model.

What would settle it

A survey measurement showing whether the monopole deviation in small voids is about ten times larger than in large voids, matching the predicted growth from 2.8% to 29.7%, would confirm or refute the central claim.

Figures

Figures reproduced from arXiv: 2605.12482 by Yue Nan.

Figure 1
Figure 1. Figure 1: FIG. 1. Void real-space profiles for [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Gravitational potential in [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Shell-level nonlinear evolution for a void center shell ( [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. NL amplification of RSD multipoles ( [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. RSD multipoles of the void-galaxy cross-correlation at [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Real-space profiles for the large void ( [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Absolute deviation ∆ [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Void-size dependence of the absolute multipole deviation ∆ [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. RSD multipole curves for all three void size classes at [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Galaxy bias sensitivity of the RSD multipole MG [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Redshift dependence of the RSD multipoles for the large void ( [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Synthetic-covariance template-Fisher S/N for the [PITH_FULL_IMAGE:figures/full_fig_p020_12.png] view at source ↗
read the original abstract

Cosmic voids provide low-density environments where the scalar fifth force predicted by $f(R)$ modified gravity can be weakly screened. We present a semi-analytical calculation of the monopole, dipole, and quadrupole of the void-galaxy cross-correlation function $\xi^{s}(s,\mu)$ in redshift space for the Hu-Sawicki $f(R)$ model ($n=1$), combining scale-dependent growth induced by the scalaron with nonlinear spherical shell dynamics. The same framework can be generalized to metric $f(R)$ theories for which $G_{\rm eff}(k,a)/G$ is specified in the quasi-static limit. Our key results are: (1)~the monopole deviation from $\Lambda{\rm CDM}$ grows from $+2.8\%$ for large voids ($r_v=30 h^{-1}{\rm Mpc}$) to $+29.7\%$ for small voids ($r_v=11.7 h^{-1}{\rm Mpc}$) at $|f_{R0}|=10^{-5}$, a distinctive size-dependent signature of the Compton-scale scalaron response, with $\lambda_C\approx 8 h^{-1}{\rm Mpc}$; (2)~nonlinear evolution amplifies the modified-gravity signal by $\mathcal{A}_0\approx 4$, bringing it within reach of ongoing and upcoming spectroscopic surveys such as DESI, Subaru PFS, Euclid, and Roman; (3) the gravitational potential contains a finite-range Yukawa component, producing a radially dependent dipole signature complementary to the density and velocity multipoles; (4) for the fiducial Hu-Sawicki evolution, the signal generally decreases toward higher redshift as the scalaron Compton wavelength becomes shorter, but remains potentially detectable at Stage-IV spectroscopic void samples. We show that the void-scale transition in the modified-gravity response, the joint sensitivity to density, velocity, and fifth-force contributions, and the nonlinear amplification around void shells make redshift-space void-galaxy multipoles a powerful semi-analytical probe of $f(R)$ gravity and effective dark-energy inhomogeneities in modified gravity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper presents a semi-analytical framework for computing the monopole, dipole, and quadrupole of the void-galaxy cross-correlation function in redshift space for the Hu-Sawicki f(R) model (n=1). It combines scale-dependent growth induced by the scalaron with nonlinear spherical shell dynamics to predict deviations from ΛCDM, including a size-dependent monopole signal that grows from +2.8% at r_v=30 h^{-1}Mpc to +29.7% at r_v=11.7 h^{-1}Mpc for |f_R0|=10^{-5}, nonlinear amplification by A_0≈4, and a Yukawa-induced dipole, with potential detectability in surveys like DESI and Euclid.

Significance. If the approximations hold, the work offers an efficient semi-analytical probe of f(R) gravity via void statistics, with a distinctive Compton-scale size dependence and nonlinear boost that could complement other tests and be accessible to Stage-IV surveys. The generalizability to other metric f(R) models where G_eff(k,a)/G is specified in the quasi-static limit is a positive feature.

major comments (2)
  1. [Framework and results sections] The headline quantitative results on monopole deviations (+2.8% to +29.7%) and nonlinear amplification A_0≈4 rest on feeding the quasi-static G_eff(k,a)/G directly into nonlinear spherical shell dynamics for the Hu-Sawicki n=1 model. Given that λ_C≈8 h^{-1}Mpc is comparable to the considered void radii, this may miss time-dependent scalaron effects or non-spherical mode coupling in underdense shells, which could alter the reported size-dependent signature (see abstract and framework description).
  2. [Results and discussion] The reported percentage deviations lack accompanying error bars, covariance estimates, or direct comparisons to N-body simulations, which is load-bearing for assessing robustness of the central claims about distinctive size-dependent signals and survey detectability, especially with post-hoc void size selections.
minor comments (1)
  1. [Notation and definitions] Clarify the exact definition and computation of the amplification factor A_0 and ensure consistent notation for λ_C throughout.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive review and positive assessment of the potential significance of our semi-analytical framework. We address each major comment in turn below, with revisions where appropriate to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Framework and results sections] The headline quantitative results on monopole deviations (+2.8% to +29.7%) and nonlinear amplification A_0≈4 rest on feeding the quasi-static G_eff(k,a)/G directly into nonlinear spherical shell dynamics for the Hu-Sawicki n=1 model. Given that λ_C≈8 h^{-1}Mpc is comparable to the considered void radii, this may miss time-dependent scalaron effects or non-spherical mode coupling in underdense shells, which could alter the reported size-dependent signature (see abstract and framework description).

    Authors: We acknowledge that our approach adopts the quasi-static limit for G_eff(k,a)/G, which is the standard approximation for f(R) models on the relevant scales and redshifts, and incorporates it into the nonlinear spherical shell equations to capture the leading effects of the fifth force. While time-dependent scalaron dynamics and non-spherical mode coupling could in principle introduce quantitative corrections when void radii approach λ_C, these are expected to be sub-dominant corrections that preserve the distinctive size-dependent signature arising from the Compton wavelength. In the revised manuscript we have expanded the framework section to explicitly discuss the validity range of the quasi-static and spherical approximations, added a paragraph on potential higher-order effects with supporting references, and included a limited comparison to existing N-body results from the literature on f(R) voids to support robustness of the reported trends. revision: partial

  2. Referee: [Results and discussion] The reported percentage deviations lack accompanying error bars, covariance estimates, or direct comparisons to N-body simulations, which is load-bearing for assessing robustness of the central claims about distinctive size-dependent signals and survey detectability, especially with post-hoc void size selections.

    Authors: As a semi-analytical calculation, the reported deviations are deterministic predictions within the model assumptions rather than statistical measurements from mocks. To improve the assessment of robustness and detectability we have revised the results and discussion sections to include survey-specific signal-to-noise estimates for DESI, Euclid and similar Stage-IV samples, drawing on published covariance models for void-galaxy correlations. We have also added direct comparisons to relevant existing N-body studies of voids in f(R) gravity. We agree that dedicated, tailored N-body validation for this specific multipole observable would be valuable and have noted this explicitly as future work. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation combines independent model inputs with spherical dynamics

full rationale

The paper's central results follow from feeding the quasi-static G_eff(k,a)/G for the Hu-Sawicki n=1 model into nonlinear spherical shell evolution to compute redshift-space multipoles. This is a forward calculation from established modified-gravity equations and symmetry assumptions rather than a fit to the reported monopole deviations or A_0 factor. No self-definitional steps, fitted-input predictions, or load-bearing self-citations appear in the derivation chain; the size-dependent signatures and nonlinear amplification emerge directly from the scalaron Compton wavelength and shell dynamics without reducing to parameters tuned inside the paper.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the Hu-Sawicki f(R) model with fixed n=1, the quasi-static limit for the scalaron, and the validity of spherical shell dynamics for void evolution; no new entities are introduced.

free parameters (2)
  • |f_R0|
    Model parameter controlling the amplitude of deviations, set to 10^{-5} for the reported signals.
  • n
    Fixed to 1 for the Hu-Sawicki model variant used throughout.
axioms (2)
  • domain assumption Quasi-static limit applies to the scalaron field allowing specification of G_eff(k,a)/G
    Invoked to generalize the framework to metric f(R) theories and compute scale-dependent growth.
  • domain assumption Nonlinear void evolution follows spherical shell dynamics
    Used to model the amplification of the modified-gravity signal around void shells.

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Reference graph

Works this paper leans on

107 extracted references · 107 canonical work pages · 60 internal anchors

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    General structure The starting point is the mapping from real-space to redshift-space coordinates for the void-galaxy cross- correlation. To distinguish the full redshift-space cor- relationξ s(s, µ) from the underlying radial profile, we writeξ vg(s)≡b δ(s) for the biased real-space void-galaxy correlation profile evaluated at the redshift-space sep- ara...

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    Monopole The monopole (ℓ= 0) follows from Eq. (25) of Ref. [26]. At lowest order in the velocity field the standard Kaiser- like formula gives ξ(0) 0 (s) =b δ(s) +b f ¯∆(s)−δ(s) + f2 3 ¯∆(s)−δ(s) , (34) wheref≡dlnD/dlnais the growth rate. The full ex- pression including the streaming (non-perturbative) cor- rections from the coherent velocity field ˜Vread...

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    Quadrupole The quadrupole (ℓ= 2) arises from the anisotropy be- tween radial and transverse motions (Eq. 26 of Ref. [26]). Its full expression is ξ2(s) = (1 +ξ vg) 2 105 −7 ˜V ′ s+ 29 ˜V ˜V ′ s + 6(˜V ′ s)2 + 6˜V ˜V ′′ s2 + ξ′ vg 105 ˜V s(−14 + 29 ˜V+ 24 ˜V ′ s) + 2 35 ˜V 2 s2 ξ′′ vg .(36) At leading order in ˜V(keeping onlyO( ˜V) terms), Eq. (36) reduces...

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